Thus the regular polyhedra come in natural pairs: the dodecahedron with the icosahedron, the cube with the octahedron, and the tetrahedron with itself.

The rest are assembled by (pasting) combinations of the regular polyhedra described earlier: the dodecahedron, the small stellated dodecahedron, the great stellated dodecahedron and the great icosahedron.

en.wikipedia.org /wiki/Polyhedral (1864 words)

Icosahedron jerak.org(Site not responding. Last check: 2007-08-31)

Finally, non-convex polytopes do not carry the same strict requirements as convex polytopes, and icosahedra are indeed the cells of the icosahedral 120-cell, one of the ten non-convex regular polychora.

Alternatively, using the nomenclature for snub polyhedra that refers to a snub cube as a snub cuboctahedron (cuboctahedron = Rectification (geometry) cube) and a snub dodecahedron as a snub icosidodecahedron (icosidodecahedron = rectified dodecahedron), one may call the icosahedron the snub octahedron (octahedron = rectified tetrahedron).

Despite appearances, when an icosahedron is inscribed in a sphere, it occupies less of the sphere's volume (60.54%) than a dodecahedron inscribed in the same sphere (66.49%).

The rhombuses correspond to the edges of a cube or octahedron, The rhombic dodecahedron is the shape obtained by trimming a cube to octagonal cross sections along all three axes, then peaking all the face centres to square pyramids.

= E. The icosidodecahedron is similarly the truncation of the dodecahedron or the icosahedron.

In other words, a platonic solid is a three dimensional shape where each face is an identical flat shape with all sides and angles the same, and the same number of these faces meet at each corner.

There are 5 platonic solids, the cube (6 squares, 3 meeting at each vertex), the tetrahedron (4 triangles, 3 meeting at each vertex), the octahedron (8 triangles, 4 meeting at each vertex), the dodecahedron (12 pentagons, 3 meeting at each vertex), and the icosahedron (20 triangles, 5 meeting at each vertex).

Less able students could be supported either by help in designing the net to make a triangular prism (2 equilateral triangles joined by three squares), or they could be provided with the net to cut out, fold and stick together.